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Fast Fourier transform algorithms for parallel computers

Author: Daisuke Takahashi
Publisher: Singapore : Springer, 2019.
Series: High-performance computing series, v. 2
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Following an introduction to the basis of the fast Fourier transform (FFT), this book focuses on the implementation details on FFT for parallel computers. FFT is an efficient implementation of the discrete Fourier transform (DFT), and is widely used for many applications in engineering, science, and mathematics. Presenting many algorithms in pseudo-code and a complexity analysis, this book offers a valuable  Read more...
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Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Daisuke Takahashi
ISBN: 9789811399657 9811399654
OCLC Number: 1122680860
Description: 1 online resource (ix, 114 pages) : illustrations
Contents: Intro; Preface; Contents; 1 Introduction; References; 2 Fast Fourier Transform; 2.1 Definitions of DFT; 2.2 Basic Idea of FFT; 2.3 Cooley-Tukey FFT Algorithm; 2.4 Bit-Reversal Permutation; 2.5 Stockham FFT Algorithm; 2.6 FFT Algorithm for Real Data; 2.6.1 FFT of Two Real Data Simultaneously; 2.6.2 n-Point Real FFT Using n/2-Point Complex FFT; References; 3 Mixed-Radix FFT Algorithms; 3.1 Two-Dimensional Formulation of DFT; 3.2 Radix-3 FFT Algorithm; 3.3 Radix-4 FFT Algorithm; 3.4 Radix-5 FFT Algorithm; 3.5 Radix-8 FFT Algorithm; References; 4 Split-Radix FFT Algorithms 4.1 Split-Radix FFT Algorithm4.2 Extended Split-Radix FFT Algorithm; References; 5 Multidimensional FFT Algorithms; 5.1 Definition of Two-Dimensional DFT; 5.2 Two-Dimensional FFT Algorithm; 5.3 Definition of Three-Dimensional DFT; 5.4 Three-Dimensional FFT Algorithm; Reference; 6 High-Performance FFT Algorithms; 6.1 Four-Step FFT Algorithm; 6.2 Five-Step FFT Algorithm; 6.3 Six-Step FFT Algorithm; 6.4 Blocked Six-Step FFT Algorithm; 6.5 Nine-Step FFT Algorithm; 6.6 Recursive Six-Step FFT Algorithm; 6.7 Blocked Multidimensional FFT Algorithms; 6.7.1 Blocked Two-Dimensional FFT Algorithm 6.7.2 Blocked Three-Dimensional FFT Algorithm6.8 FFT Algorithms Suitable for Fused Multiply-Add (FMA) Instructions; 6.8.1 Introduction; 6.8.2 FFT Kernel; 6.8.3 Goedecker's Technique; 6.8.4 Radix-16 FFT Algorithm; 6.8.5 Radix-16 FFT Algorithm Suitable for Fused Multiply-Add Instructions; 6.8.6 Evaluation; 6.9 FFT Algorithms for SIMD Instructions; 6.9.1 Introduction; 6.9.2 Vectorization of FFT Kernels Using Intel SSE3 Instructions; 6.9.3 Vectorization of FFT Kernels Using Intel AVX-512 Instructions; References; 7 Parallel FFT Algorithms for Shared-Memory Parallel Computers 7.1 Implementation of Parallel One-Dimensional FFT on Shared-Memory Parallel Computers7.1.1 Introduction; 7.1.2 A Recursive Three-Step FFT Algorithm; 7.1.3 Parallelization of Recursive Three-Step FFT; 7.2 Optimizing Parallel FFTs for Manycore Processors; 7.2.1 Introduction; 7.2.2 Parallelization of Six-Step FFT; 7.2.3 Performance Results; References; 8 Parallel FFT Algorithms for Distributed-Memory Parallel Computers; 8.1 Implementation of Parallel FFTs in Distributed-Memory Parallel Computers; 8.1.1 Parallel One-Dimensional FFT Using Block Distribution 8.1.2 Parallel One-Dimensional FFT Using Cyclic Distribution8.1.3 Parallel Two-Dimensional FFT in Distributed-Memory Parallel Computers; 8.1.4 Parallel Three-Dimensional FFT in Distributed-Memory Parallel Computers; 8.2 Computation-Communication Overlap for Parallel One-Dimensional FFT; 8.2.1 Introduction; 8.2.2 Computation-Communication Overlap; 8.2.3 Automatic Tuning of Parallel One-Dimensional FFT; 8.2.4 Performance Results; 8.3 Parallel Three-Dimensional FFT Using Two-Dimensional Decomposition; 8.3.1 Introduction
Series Title: High-performance computing series, v. 2
Responsibility: Daisuke Takahashi.

Abstract:

Following an introduction to the basis of the fast Fourier transform (FFT), this book focuses on the implementation details on FFT for parallel computers. Chapter 5 explains multi-dimensional FFT  Read more...

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